Frostbite deals double damage to champions "slowed by an ice effect." This seems to imply that any ice effect should work, but the forums seem divided on the matter.
It obviously works with Anivia's own skills, as otherwise it would be pointless. Check off Flash Frost, and Glacial Storm.
Very few people seem to think that the damage doubles against champions effected by items. Items that seem to slow via frost are Rylai's Crystal Scepter, and Iceborn Gauntlet.
There are a number of champions with ice-based slows, and this list seems more divisive, some threads seem to claim a subset, some claim them all, and some claim none of them. Those I can think of are:
- Sejuani; Frost, Permafrost
- Ashe; Frost Shot, Volley (sometimes), Enchanted Crystal Arrow
- Nunu; Ice blast, Absolute Zero